Groupe de Travail

Organisateur : Patrick LE MEUR, Dominique MANCHON et Jean-Marie LESCURE

Les exposés ont lieu le vendredi à 14h00 en salle 2222 du bâtiment de mathématiques (consulter le plan d'accès au laboratoire).

 2003 / 2004 2004 / 2005 2005 / 2006 2006 / 2007 2007 / 2008 2008 / 2009 2009 / 2010 2010 / 2011 2011 / 2012

Prochain séminaire......
 le Vendredi 21 juin 2013 - RelÃ¢che (journÃ©es dualitÃ© et algÃ¨bre non-commutative)

 Juillet 2013

• Vendredi 05 juillet 2013 - Rufus Willett (UniversitÃ© de Hawaii)

Ghosts, monsters, and exact crossed products

Ghost operators are 'nearly compact' operators on Hilbert space. Ghost operators in crossed product (and related) C*-algebras associated to so-called 'Gromov monster' groups give rise to pathological properties in the associated K-theory groups. As an application, all known counterexamples to the Baum-Connes conjecture with coefficients arise in essentially this way. I'll discuss geometric conditions leading to the existence of ghosts (related to expanding graphs and property (T)), and some ways to ameliorate the problems caused by ghosts using the idea of exactness. This is joint work with John Roe, and with Paul Baum and Erik Guentner.

 Juin 2013

• Vendredi 28 juin 2013 - Pierre Clavier (LPTHE Paris 6 Jussieu)

On s'intÃ©ressera Ã  l'Ã©quation de Schwinger-Dyson du modÃ¨le de Wess-Zumino de masse nulle. AprÃ¨s avoir Ã©crit cette Ã©quation sous forme diffÃ©rentielle, on extraira le comportement asymptotique de ses solutions. Cela nous permettra d'utiliser un ansatz qui simplifiera les calculs en sÃ©parant les solutions en diffÃ©rentes composantes, chacune avec un comportement distinct. Enfin nous verrons comment des zÃ©tas apparaissent dans les solutions.

• Vendredi 14 juin 2013 - Kevin Langlois (UJF Grenoble)

• Jeudi 06 juin 2013 - 14h - Nigel Higson, UniversitÃ© d'Ã‰tat de Pennsylvanie.

Contractions of Lie Groups and Representation Theory

The contraction of a Lie group G to a subgroup K is a Lie group that approximates G to first order near K. It is usually easier to understand than G itself. The name "contraction" comes from the mathematical physicists, who examined the Galilean group as a contraction of the Poincare group of special relativity. My focus will be on a related but different class of examples: the prototype is the group of isometric motions of Euclidean space, viewed as a contraction of the group of isometric motions of hyperbolic space. It is natural to expect some sort of limiting relation between representations of the contraction and representations of G itself. But in the 1970s George Mackey discovered an interesting rigidity phenomenon: as the contraction group is deformed to G, the representation theory remains in some sense unchanged. In particular the irreducible representations of the contraction group parametrize the irreducible representations of G. I shall formulate a reasonably precise conjecture along these lines that was inspired by subsequent developments in C*-algebra theory and noncommutative geometry, and describe the evidence in support of it, which is by now substantial. However a conceptual explanation for Mackey's rigidity phenomenon remains elusive.

 Mai 2013

• Vendredi 31 mai 2013 - Quimey Vivas (Universidad de Buenos Aires)

Automorphisms and isomorphisms of quantum generalized Weyl algebras

• Vendredi 24 mai 2013 - Simon Riche (CNRS UBP)

• Vendredi 10 mai 2013 - Rene Schulz (VisioconfÃ©rence depuis GÃ¶ttingen)

Global Fourier integral operators via tempered oscillatory integrals with inhomogeneous phase functions

The theory of global Fourier integral operators is a field of active research, with many open questions. In our approach, we study certain families of oscillatory integrals, parametrised by phase functions and amplitude functions globally defined on the Euclidean space, which give rise to tempered distributions, avoiding the standard homogeneity requirement on the phase function. The singularities of these distributions are described both from the point of view of the lack of smoothness as well as with respect to the decay at infinity. In particular, the latter will depend on a version of the set of stationary points of the phase function, including elements lying at the boundary of the radial compactification of the Euclidean space. We then consider classes of global Fourier integral operators on the Euclidean space, defined in terms of kernels of the form of such oscillatory integrals. As an example we consider the solution operator of the Klein Gordon equation. This talk is based on joint work with Sandro Coriasco from the University of Torino, Italy.

 Avril 2013

• Vendredi 05 avril 2013 - Ali Baklouti (FacultÃ© des Sciences de Sfax)

ReprÃ©sentations monomiales de type discret sur les groupes de Lie rÃ©solubles exponentiels.

Dans cet exposÃ©, je vais poser quelques problÃ¨mes reliÃ©s Ã  une reprÃ©sentation monomiale $\tau ={ind}_H^G \chi$ oÃ¹ $G$ dÃ©signe un groupe de Lie rÃ©soluble exponentiel, $H$ un sous-groupe analytique et $\chi$ un caractÃ¨re unitaire de $H$. Je vais me concentrer sur la situation oÃ¹ les multiplicitÃ©s de $\tau$ sont de type discret et donner un contre-exemple Ã  une conjecture posÃ©e par Michel Duflo dans ce contexte.

 Mars 2013

• Vendredi 29 mars 2013 - Amaury Freslon (en VisioconfÃ©rence depuis Metz)

Operator-valued inequalities in noncommutative harmonic analysis

Computing the norm of a linear map on a C*-algebra is a very difficult problem in general, because it requires fine estimates for the norm of many elements of the algebra. However, if the C*-algebra comes from the regular representation of a group, harmonic analysis provides us with powerful tools to estimate the norms. We will recal these tools and then adress the case of discrete quantum groups, where noncommutative harmonic analysis is again the key to useful norm estimatates. Our main goal is to use these tools to prove approximation properties and structure results on the operator algebras associated to these quantum groups.

• Vendredi 22 mars 2013 - Dominique Manchon (CNRS-UBP)

Graphes de Feynman et structures extÃ©rieures (2Ã¨me partie)

• Vendredi 15 mars 2013 - FranÃ§ois Gautero (UniversitÃ© de Nice)

Pavages, mesures invariantes et norme de Thurston asymptotique

• Vendredi 01 mars 2013 - Olivier Gabriel (GÃ¶ttingen)

Lie group actions, spectral triples and generalised crossed products

The aim of this talk is to generalise the constructions of spectral triples on noncommutative tori and Quantum Heisenberg Manifolds (QHM) to broader settings. After a few reminders about noncommutative tori and spectral triples, we prove that an ergodic action of a compact Lie group G on a unital C*-algebra A yields a natural spectral triple structure on A. In the second part, we investigate "permanence properties" for the previous sort of spectral triples. We first introduce the notion of Generalised Crossed Product (GCP) and illustrate it by the case of QHM. A GCP contains a sub-C*-algebra called its "basis". A spectral triple on the basis can induce a spectral triple on the GCP, under some assumptions which we make explicit. This talk is based on work in progress in collaboration with M. Grensing. If time permits, we will relate these new results to our previous work in this direction.

 Février 2013

• Vendredi 22 février 2013 - MichaÃ«l Bulois (ICJ et UniversitÃ© Jean Monnet, St Etienne)

• Vendredi 08 février 2013 - Sonia Natale (Cordoba, Argentine)

On weakly group-theoretical non-degenerate braided fusion categories

We shall discuss some results on the structure of the class of braided fusion categories of the title, in particular, concerning their class in the Witt group of non-degenerate braided fusion categories introduced by Davydov, Mueger, Nikshych and Ostrik. We shall also present some results that give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects, which imply that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a small natural number is indeed weakly group-theoretical.

• Vendredi 01 février 2013 - Rachel Taillefer

Je vais vous parler de certaines algÃ¨bres qui gÃ©nÃ©ralisent les algÃ¨bres de Nakayama symÃ©triques, en donner une description par carquois et relations puis une classification Ã  Ã©quivalence dÃ©rivÃ©e prÃ¨s, en vous prÃ©sentant certains outils que nous avons utilisÃ©s. C'est un travail en commun avec Nicole Snashall.

 Janvier 2013

• Vendredi 25 janvier 2013 - Patrick le Meur (UBP)

• Vendredi 18 janvier 2013 - Dominique Manchon (CNRS/UniversitÃ© Blaise Pascal)

Graphes de Feynman et structures extÃ©rieures

• Vendredi 11 janvier 2013 -

RelÃ¢che

 Décembre 2012

• Vendredi 14 décembre 2012 - Martijn Caspers (BesanÃ§on)

Quantum groups, Lp-spaces and Fourier theory

In this talk we address several questions related to quantum groups and non-commutative Lp-spaces. We introduce Fourier transforms on non-commutative Lp-spaces associated with a quantum group. We show that it is imperative to use the techniques of Lp-spaces constructed on type III von Neumann algebras, even if we are dealing with the semi-finite case. We find a spherical analogue of the Fourier transform and are able to describe it explicitly in the case of "extended-SUq(1,1)". This involves the so-called quantum Duflo-Moore operators.

• Vendredi 07 décembre 2012 - Charlotte Wahl (Hannover, en visioconfÃ©rence depuis Potsdam)

Rho-invariants and the classification of differential structures on closed manifolds

In her talk, Sara Azzali explained the use of rho-invariants associated to the spin Dirac operator for the classification of metrics with positive scalar curvature. Analogously, rho-invariants associated to the signature operator can be used to distinguish differential structures on closed manifolds. However, since the signature operator is not invertible in general, their study tends to be more difficult. I will discuss three types of rho-invariants - the L^2-rho-invariants of Cheeger and Gromov, Lott's higher rho-invariants and the rho-invariants associated to 2-cocycles studied by Sara Azzali and myself and I will explain what is known about their properties for the signature operator.

 Novembre 2012

• Vendredi 30 novembre 2012 - Seunghun Hong (GÃ¶ttingen). Horaire exceptionnel : 13h15

A Lie-algebraic approach to the local index theorem on compact homogeneous spaces

Using a K-theory point of view, Bott related the Atiyah-Singer index theorem for elliptic operators on compact homogeneous spaces to the Weyl character formula. In this talk, I will explain how to prove the local index theorem for compact homogenous spaces using Lie algebra methods. The method follows in outline the proof of the local index theorem due to Berline and Vergne. But the use of Kostant's cubic Dirac operator in place of the Riemannian Dirac operator leads to substantial simplifications. An important role is also played by the quantum Weil algebra of Alekseev and Meinrenken.

• Vendredi 23 novembre 2012 - Yves Stalder (Clermont-Ferrand)

Actions hautement transitives des produits libres

Soit G un groupe dÃ©nombrable opÃ©rant sur un ensemble (infini) X. L'action est dite hautement transitive si elle est k-transitive pour tout entier naturel k, ce qui revient Ã  dire que l'image de G dans le groupe Sym(X) est dense. Dixon a prouvÃ© par des mÃ©thodes de gÃ©nÃ©ricitÃ© au sens de Baire que les groupes libres non abÃ©liens possÃ¨dent des actions fidÃ¨les et hautement transitives. J'expliquerai comment exploiter ses idÃ©es pour dÃ©terminer les produits libres qui possÃ¨dent des actions fidÃ¨les et hautement transitives. C'est un travail commun avec Soyoung Moon.

• Vendredi 16 novembre 2012 - Sara Azzali (Paris 7)

Invariants eta et courbure scalaire positive

 Octobre 2012

• Vendredi 26 octobre 2012 - Ivan Angiono (Cordoba, Argentine)

Finite pointed tensor categories over abelian groups

It is known that the category of representations of a Hopf algebra is a tensor category. But there are tensor categories which are not equivalent to the category of representations of a Hopf algebra. In this context Drinfeld introduced the notion of quasi Hopf algebra in 1990. Moreover Etingof and Ostrik characterized those tensor categories coming from quasi Hopf algebras as categories whose objects have integer Frobenius Perron dimensions. It is interesting to know then examples of quasi Hopf algebras which are not Hopf algebras. Gelaki defined a few years ago a family of quasi Hopf algebras over cyclic groups and proved in a joint work with Etingof that this covers all the examples of finite tensor categories with cyclic group of invertible objects with prime order. In this talk we will present an extension of this classification for a more general family of cyclic groups, extending the results of Etingof-Gelaki, and a nice way to construct more examples of finite-dimensional quasi-Hopf algebras with abelian group of invertible objects; it involves de-equivariantization of Hopf algebras.

• Vendredi 19 octobre 2012 - Peng Shan (Caen)

AlgÃ¨bres de Lie affines et algÃ¨bres de Cherednik cyclotomiques

Varagnolo et Vasserot ont conjecturÃ© une Ã©quivalence de catÃ©gories entre un catÃ©gorie O parabolique d'algÃ¨bres de Lie affines de gl et la catÃ©gorie O d'algÃ¨bres de Cherednik cyclotomiques. J'expliquerai une dÃ©monstration de cette conjecture et quelques applications. Ceci est un travail en commun avec R. Rouquier, M. Varagnolo et E. Vasserot.

• Vendredi 12 octobre 2012 - Elmar Schrohe (Hannover, en visio-confÃ©rence depuis Potsdam)

A Families Index Theorem for Boundary Value Problems

• Vendredi 05 octobre 2012 - Claire Renard (ENS Cachan)

 Septembre 2012

• Vendredi 28 septembre 2012 - Robin Deeley (Goettingen)

Relative constructions in geometric K-homology

K-homology provides a useful framework for the study of problems from index theory. The Baum-Douglas (i.e., (M,E,phi)) model provides a geometric realization of K-homology. After introducing this model, we will discuss a number of "relative" constructions within the framework of geometric K-homology. We will also show how a number of interesting index theorems arise from such constructions. Two examples are the Freed-Melrose index theorem and an R/Z-valued index theorem which is similar to the index theorem for flat vector bundles of Atiyah-Patodi-Singer.

 Directeur Michael Heusener Tél : +33 (0)4 73 40 77 38 Directeur adjoint Jean Picard Tél : +33 (0)4 73 40 70 61 Secrétariat Valérie Sourlier Tél : +33 (0)4 73 40 70 50 Fax : +33 (0)4 73 40 54 50 Informatique Damien Ferney Tél : +33 (0)4 73 40 70 68 Cédric Barrel Tél : +33 (0)4 73 40 70 55 Adresse Université Blaise Pascal - Laboratoire de Mathématiques UMR 6620 - CNRS Campus des Cézeaux - B.P. 80026 63171 Aubière cedex France   Tél : +33 (0)4 73 40 70 50 Fax : +33 (0)4 73 40 70 64